Unsure what kind of problem this is

1. The problem statement, all variables and given/known data
Sydney places three markers at the points (0,0), (1,0) and (0,1) on a sheet of graph paper. She then repeatedly "jumps two of the markers over each other," meaning that the old and new positions are located at four evenly spaced points along a line, as shown. After a while two of the markers are located at (63,-2) and (-108,16). Where is the third?

2. Relevant equations
I'm not sure what equations I'm supposed to use

3. The attempt at a solution
I graphed it on my graph paper, i'm guessing it has to do something with the distance formula ?

Sydney places three markers at the points (0,0), (1,0) and (0,1) on a sheet of graph paper. She then repeatedly "jumps two of the markers over each other," meaning that the old and new positions are located at four evenly spaced points along a line, as shown. After a while two of the markers are located at (63,-2) and (-108,16). Where is the third?